After much diagnosis and a decent amount of poking/prodding, I was able to determine that this particular Roomba had two problems. One of the wheel encoders was not functioning properly, and one of the wheel drop sensors was totally broken. Getting the Roomba disassembled to a point where further analysis could be done was not impossible but it did take care and patience. I highly recommend following the service manual to help in these efforts.
With the aid of a magnifying headset I was able to scrutinize the wheel drop sensors for potential problems. As can be seen here, there was plenty of corrosion to the point where the spring in the micro switch was no longer functioning. A quick visit to eBay had the part ordered in no time.
|Crusty Old Switch|
I disassembled the motor assembles for both wheels and gave them a good cleaning. I used extra care while cleaning the encoder wheel and sensors.
In the end it would turn out that one of the wheels had indeed gone bad. Another trip to eBay had two new wheel assemblies ordered at the price of seventeen dollars US. Both parts had came and they were immediately installed. When everything was back together the Roomba passed the diagnostic tests with flying colors. Below is a video of a test drive.
It was now time to get the firmware upgraded. Luckily I found someone online who was willing to loan/rent an Osmo upgrade unit to me. Once that came in the mail I went ahead and upgraded the firmware.